Cost-effectiveness of different monitoring strategies in a screening and treatment programme for hepatitis B in The Gambia

Background Clinical management of chronic hepatitis B virus (HBV) infection is complex and access to antiviral treatment remains limited in sub-Saharan Africa. International guidelines recommend monitoring at least annually for disease progression among HBV-infected people not meeting treatment criteria at initial diagnosis. This study aimed to assess the impact and cost-effectiveness of alternative strategies for monitoring. Methods We used a mathematical model of HBV transmission and natural history, calibrated to all available West African data, to project the population-level health impact, costs and cost-effectiveness of different monitoring strategies for HBV-infected individuals not initially eligible for antiviral treatment. We assumed that these patients were found in the year 2020 in a hypothetical community-based screening programme in The Gambia. Monitoring frequencies were varied between every 5 and every 1 year and targeted different age groups. Results The currently recommended annual monitoring frequency was likely to be not cost-effective in comparison with other strategies in this setting. 5-yearly monitoring in 15-45-year olds, at US$338 per disability-adjusted life year averted, had the highest probability of being the most effective cost-effective monitoring strategy. Conclusions Monitoring less frequently than once a year is a cost-effective strategy in a community-based HBV screening and treatment programme in The Gambia, with the optimal strategy depending on the cost-effectiveness threshold. Efficiencies may be gained by prioritising the 15-45-year age group for more intensive monitoring.


Data sources
All data sources used for model parameterisation and calibration are summarised in Table   S1, with references shown below.  [3,4] Disease progression in liver disease patients

Prevalence of different infection and disease states in chronic HBV carriers
The Gambia [4,16] Cross-sectional characteristics of liver disease patients Prevalence of HBeAg in cirrhosis and HCC patients, mean age and percentage of male sex among cirrhosis and HCC patients, percentage of deaths due to endstage liver disease, prevalence of compensated and decompensated cirrhosis in HCC patients The Gambia [20,22,40,42] 28. Whittle     (hepatitis b or hbv or hep B or (type b adj1 hepatitis) or hbsag or hbs-ag or hbs antigen* or "hepatitis virus* B" or hbvcoinfected or hbv-coinfected or hbv-co-infected or hbvinfect* or hbvinfect* or hbvpositive* or hbvrelated or hbvcarrier* or hiv?hbv or hbv?hiv).mp. [mp=title, abstract, original title, name of substance word, subject heading word, keyword heading word, protocol supplementary concept word, rare disease supplementary concept word, unique identifier, synonyms] #3 1 or 2 #4

A. Data assembly
exp "AFRICA SOUTH OF THE SAHARA"/ #5 (africa* or SSA or angola* or benin* or botswana* or burkina faso* or burundi* or cabo verd* or cameroon* or cape verd* or central african republic* or chad* or comoros or comoro or comoroan or comores or comorean or (congo* not congo red) or cote divoir* or democratic republic of the congo* or djibouti* or equatorial guinea* or eritrea* or ethiopia* or gabon* or gambia* or ghan* or (guinea* not guinea pig* not guinea worm*) or guinea-bissau* or ivory coast or kenya* or lesotho* or liberia* or madagascar* or malawi* or mali or maurit* or mauritania* or mozambi* or namibia* or niger* or nigeria* or rwanda* or (sao tome and principe*) or senegal* or seychelle* or sierra leone* or somali* or south africa* or south sudan* or (sudan* not sudan blue) or swazi* or tanzania* or togo* or uganda* or zambia* or zimbabwe*).mp. [mp=title, abstract, original title, name of substance word, subject heading word, keyword heading word, protocol supplementary concept word, rare disease supplementary concept word, unique identifier, synonyms] #6 4 or 5 #7 3 and 6 #8 Liver Cirrhosis/ or Liver Cirrhosis, Biliary/ or Liver Diseases/ or exp Hepatic Insufficiency/ or HEPATITIS/ or Hepatitis, Chronic/ or Liver Neoplasms/an, bl, cl, co, di, ec, ep, et, hi, mi, mo, pa, pc, sn or Adenoma, Liver Cell/an, bl, cl, co, di, ec, ep, et, hi, mi, mo, pa, pc, sn or Carcinoma, Hepatocellular/an, bl, cl, co, di, ec, ep, et, hi, mi, mo, pa, pc, sn #9 (cirrhosis or cirrhotic* or liver fibrosis or liver cancer* or hepatocellular carcinoma* or liver cell carcinoma* or hepatic carcinoma* or hepatic cell carcinoma* or hepatocellular cancer or liver disease* or liver failure* or liver inflammation* or liver necroinflammation*).mp. [mp=title, abstract, original title, name of substance word, subject heading word, keyword heading word, protocol supplementary concept word, rare disease supplementary concept word, unique identifier, synonyms] #10 8 or 9 #11 6 and 10 #12 7 or 11 #13 12 and "Case Reports" [Publication Type] #14 12 and "Letter" [Publication Type] #15 12 not 13 not 14

Study selection and inclusion criteria
Initial study selection for the evidence map was based on screening of titles and abstracts by one reviewer. To be included, abstracts had to present primary data and be broadly relevant to at least one of the aspects of the research aim. Articles were therefore excluded because of being a different publication type (e.g. literature reviews, case reports, letters, etc.), if their content was not related to HBV or potentially HBV-associated liver disease, covered basic research (i.e. experimental studies on biological processes), was conducted in non-human animals, or was not conducted in a sub-Saharan African population. Articles for which no abstract could be found were also excluded, as this was usually the case for older publications that were not available online. Additionally, although the evidence map is based on primary data, other original research articles (systematic reviews, modelling studies and economic evaluations) were reviewed separately. No language or time restrictions were applied. prospective studies on disease progression in chronic HBV infection in Africa [4], but studies of liver disease attributed entirely to a cause other than HBV (e.g. hepatitis C) were excluded.
Studies reporting data related to transmission or infection incidence were included unless they were set in specific risk groups for HBV infection, e.g. healthcare workers or disease patients at risk of iatrogenic transmission.
Outcomes. HBsAg seroprevalence studies, with or without assessment of risk factors for HBV exposure or infection, were not systematically included because of multiple existing systematic reviews and meta-analyses on this [5]. For the same reason, cross-sectional studies exclusively reporting co-infection prevalence (e.g. most commonly with HIV, hepatitis C or hepatitis delta virus) were also excluded [6,7]. in addition to studies on anti-HBc IgM prevalence (indicating acute infection). All other outcomes relevant to the research question were included.

Data extraction for the model
Of 5972 individual studies found in the search, 759 studies on epidemiology or natural history met the initial inclusion criteria for the evidence map as well as for potential use in the model in the title-and-abstract screening (Figure S2.1). Analysis of the evidence map, including fulltext screening and extraction of data from a subset of the longitudinal studies, allowed to geographically and topically focus the second stage of the scoping review. Having identified The Gambia as the country with among the largest number of studies and the highest-quality data, including a longitudinal study on disease progression in chronic HBV carriers with longterm follow-up [8], cross-sectional data from The Gambia and longitudinal data on disease progression from West Africa were extracted from 53 articles for use in a mathematical model of HBV transmission and natural history. Systematic reviews spanning multiple countries or regions identified in the evidence map additionally provided data sources of mother-to-child transmission risk [2] and modelled country-specific incidence rates of hepatocellular carcinoma (HCC) [9,10] and cirrhosis mortality [11,12]. Data from the included studies were extracted stratified by age, sex and time where available.
The mean or median age of study participants was extracted where reported, or alternatively the mid-point of the age range or median based on the age distribution. Additional information on study design, setting and other relevant methods were also extracted specific to the type of data. If the included study did not specify the time period of data collection, it was assumed based on recruitment and maximum follow-up time or to be 2 years before the publication date. In studies of liver disease, all cases of primary liver cell carcinoma were assumed to represent HCC. Where possible, cirrhosis patients were classified as compensated or decompensated, based on appropriate definitions in the paper or on the reported prevalence of different clinical symptoms or scores.
Due to the large quantity of different types of data and outcomes, quality was not explicitly scored for each study. However, key considerations relevant to the different outcomes were taken into account and some studies with methodological flaws were excluded following extraction (e.g. [13]). Seven identified studies on the impact of HBV treatment were either used to inform the treatment model structure [14,15], or excluded because they involved outdated treatment regimens. All data that could not be meaningfully applied in the model structure, such as measurement of viral load or alanine aminotransferase (ALT) in isolation or on occult infection, were also excluded. Due to the overlap in papers of the long-term HBV studies conducted in The Gambia, it was not always possible to ascertain or ensure independence of the included datapoints. However, where this was of concern, the included datapoints were chosen based on containing more information (e.g. age-or sex-strata), being more recent or being based on the largest sample size.
95% confidence intervals (CI) were calculated for all extracted datapoints according to standard statistical formula where these were not reported in the original study, except for survival curves and for rates where the necessary information was not available. For proportions, the binomial 95% CI was calculated using the Wilson method, as many of the datapoints were based on small sample sizes. For rates, the 95% CI were calculated using the normal approximation of the Poisson distribution [16].

B. Model development Model structure: overview and key features
Evidence from the scoping review was used to develop a dynamic deterministic compartmental model of HBV transmission and natural history adapted to the West African epidemic in R statistical software [17]. The model was adapted from an existing structure [3] and fully structured by age and sex to represent the long-lasting duration and age-and sexdependent processes in development of chronic HBV infection and liver disease. The model was formulated using partial differential equations with respect to time and age, which were solved using the deSolve package.

Susceptible
Negative for HBsAg and anti-HBc and anti-HBs.
Never exposed to HBV.

Chronic infection compartments
Positive for HBsAg and anti-HBc, negative for anti-HBs. Some compartments are positive for HBeAg.
Chronically infected following exposure to HBV.

Recovered/Immune (before vaccine introduction)
Positive for anti-HBc and anti-HBs, negative for HBsAg.
Ever exposed to HBV. May reflect recovery from acute infection without development of chronic infection or HBsAg loss/serological recovery after chronic infection.

Recovered/Immune (after vaccine introduction)
Positive for anti-HBs, negative for HBsAg. May be positive for anti-HBc (following exposure, but not after vaccination). Ever exposed to HBV or ever vaccinated against HBV.
Transition rates in the model can vary by age (a), time (t) or sex (index g). All compartments experience the same age-, sex-and time-specific background mortality rate ( , ) and net migration rate ( , ).
Births occur into the Susceptible or the HBeAg-positive infection compartment, the latter representing mother-to-child transmission. Susceptible individuals are infected at the force of infection ( , ), of which an age-dependent proportion ( ) develop chronic carriage following acute infection, and a proportion 1 − ( ) of infected people recover from acute infection and become immune to reinfection. The force of infection varies by age to account for horizontal transmission in sub-Saharan Africa historically occurring mainly among young children [18], but potential heterogeneity in the risk of infection by population group or sub-national location was not modelled. Infectiousness depends on a carrier's HBeAg serostatus [3,20].

Sequelae and mortality from chronic HBV infection
Among carriers with chronic HBV infection, CHB compartments contain carriers with underlying liver fibrosis which can progress to compensated cirrhosis, marking the onset of the liver disease pathway to decompensation and HCC. While HCC is often a consequence of liver scarring and inflammation, it can also occur as a result of viral DNA integration into liver cells in chronic HBV infection. Therefore, all chronic infection compartments can also progress to HCC at different rates without development of cirrhosis. HBV-related mortality occurs from the compensated cirrhosis, decompensated cirrhosis and hepatocellular carcinoma compartments. From a clinical perspective, symptoms often only occur once patients reach the decompensated cirrhosis or HCC stage. HBV-related mortality from acute infection or other sequelae that may lead to death, such as renal disease, were not accounted for as these are rare compared to liver disease mortality [21,22].

HBV interventions in The Gambia
In The Gambia, 3-dose HBV infant vaccination was introduced into the national routine vaccination schedule within the Expanded Programme on Immunizations (EPI) in 1990 [23].
In the model, susceptible children are vaccinated from the year of vaccine introduction onwards, with vaccination assumed to occur at historical coverage levels reported by the World Health Organization (WHO) [24].
We assumed infant vaccination to be the only currently implemented HBV intervention in The Gambia, and that historical or current coverage of timely birth dose vaccination and antiviral treatment is negligible. Though the EPI schedule in The Gambia includes an official birth dose vaccination policy, the model structure makes the assumption that the birth dose vaccine is only effective at preventing mother-to-child transmission (MTCT) if administered within 24 hours of birth. This simplified assumption was based on indirect evidence for an increasing risk of infection with child's age at first dose between 1-4 days [25], and further observations on the need for timely administration of hepatitis B immune globulin (HBIG) [26], as there is no direct evidence from clinical trials on the efficacy of later administration of the birth dose vaccine. At the time of model development, country-reported estimates of birth dose coverage were high, but did not distinguish between a "timely" (within 24 hours of birth) and delayed administration [27]. In the most recent Gambian study on the topic, the coverage of timely delivery of the birth dose was reported to be very low between 2004 and 2014, with only 1.1% of newborns in the Farafenni region receiving the HBV vaccine at birth [28]. Similarly, in 2016, only 7% of infants born in the sampled healthcare facilities received the birth dose vaccine within 24 hours [29]. In the model, the efficacy of early vaccination (e.g. delayed birth dose vaccination) in preventing horizontal infections is captured in the application of the infant vaccine, which in itself produced model fits consistent with the low HBsAg prevalence observed in young children. New data stratified by timing of administration has since shown that scale-up of timely birth dose vaccination is already underway [27], estimating a 35% coverage in The Gambia in 2019, but this is unlikely to affect simulations of a treatment programme in adults in 2020.
Non-HBV-related treatment for early-stage liver disease, such as liver transplantation, was not included in the model as access to this is extremely limited in sub-Saharan Africa [30]. A small number of HBV carriers in The Gambia are currently taking antiviral therapy against HBV, such as study participants in the PROLIFICA screen-and-treat programme [15] and some receiving treatment for HIV co-infection [31]. However, in general access to HBV testing and treatment is still very limited, with estimates of less than 1% of HBV carriers being diagnosed and less than 1% of treatment-eligible carriers receiving treatment in The Gambia in 2016 [32].
For this reason, large-scale diagnosis and treatment for HBV infection were modelled only as hypothetical future interventions.

Modelling screening and treatment
Carriers in the HBeAg-positive infection, HBeAg-positive and -negative CHB and the compensated and the decompensated cirrhosis stages would be eligible for HBV-specific treatment according to European liver association guidelines [22], to reduce the progression of liver disease and development of HCC. For these carriers, the option of lifelong antiviral therapy with tenofovir disoproxil fumarate (TDF) was added to the model.  To solve the partial differential equations using the deSolve package in R, the age variable was discretised into 0.5 year groups from 0 to 100 to obtain a set of ordinary differential equations that can be solved with the ode.1D function using the method of lines. The aging process in the model (like all transitions in the model) therefore follows an exponential distribution, whereby all individuals within a 0.5 year age group have the same chance of aging into the next age group. The differential equations were solved numerically using the lsoda integration algorithm. Partial differential equations for the diagnosed (untreated) compartments:

Demography
As chronic HBV infection is a long-lasting infection and many of the key events in the natural history are age-specific, the transmission model was developed to reproduce the population age structure and demographic processes of The Gambia. According to standard demographic theory, the population dynamics were modelled using time-, age-and sexspecific mortality, fertility and net migration rates. These were parameterised using country-

Parameter Description Source ( , )
Age-, sex-and time-specific mortality rate Extracted central death rate m(x,n) from abridged life tables datasets.

( , )
Age-and time-specific fertility rate Extracted from age-specific fertility rates dataset. Sex-specific proportion of births Calculated from sex ratio at birth dataset.

( , )
Age-, sex-and time-specific net migration rates Calculated from age-specific survival ratio S(x,n) in abridged life tables datasets and the agespecific population size in 5-year time periods using the forward survival method.

Transmission
Two transmission routes from chronically infected to susceptible people are represented: horizontal transmission across the whole population with age-dependent mixing, and vertical transmission from mother to child, with infectivity of a carrier depending on their HBeAg serostatus. The transmission structure and prior ranges for the transmission parameters reflect pre-vaccination HBV epidemiology in sub-Saharan Africa, where the main source of new chronic infections was horizontal transmission in young children [3,20,62]. Following infection, progression to the chronic carrier states additionally depends on the age-specific risk of chronic carriage p(a), which is highest in the youngest age groups [1].

Force of infection due to horizontal transmission
The rate of acquiring (acute) infection through horizontal transmission depends on age and follows a broad age structure, adapted from Nayagam et al. 2016 [3] and Edmunds et al. 1996 [20]. The force of infection λ(a,t) was assumed to be constant within the four discrete age Since transmission is stratified into 4 discrete age groups indexed j = 1,…,4, we use notation ( ), which is the force of infection for infection among individuals in age group j.
Where corresponds to the symbols in Figure S2.4, is the total population in age group s, is the relative infectiousness of untreated HBeAg-positive compared to untreated HBeAgnegative carriers, is the relative infectiousness of treated carriers compared to untreated HBeAg-negative carriers, and: The full compartment names can be found in Table S2.3. Based on knowledge of HBV transmission dynamics, the force of infection in the model depends on the proportion of infectious individuals and is therefore not influenced by the growth of the Gambian population over time [20].
Key assumptions in the transmission structure are that: infants younger than 6 months do not participate in horizontal transmission (they can only be infected at birth through MTCT, as described below).
there is no horizontal transmission between adults (aged 15+ years) and young children (<5 years).
susceptible young children (age 0.5-5 years) are horizontally infected from other children their age at a rate β1 and from older children (age 5-15 years) at a rate β2.
susceptible older children (age 5-15 years) are horizontally infected from other children their age and younger children at a rate β2, and from adults (age 15+ years) at a rate β3.
susceptible adults (age 15+ years) are horizontally infected from older children (age 5-15 years) and other adults at a rate β3.
Priors for the β parameters were chosen so that β1> β2 and β1> β3.
For implementation of different prevention interventions, the transmission structure was designed to impose a clear distinction between horizontal and vertical transmission routes by allowing parent-to-child transmission through MTCT only. Conversely, the effective contact rate among adults and between adults and older children reflects a range of possible transmission routes such as transmission within the household, sexual and iatrogenic transmission. These were not explicitly represented, as they were assumed to contribute comparatively little to the sub-Saharan transmission dynamics of chronic infection.
Heterogeneity in behaviour e.g. in sexual interactions was therefore not included.

Births and mother-to-child transmission
Mother-to-child transmission is assumed to occur exactly at birth from HBsAg-positive mothers to some of their children, so babies are born either into the susceptible (compartment S) or the first chronic carrier stage (compartment Ie), dependent on reported risks of mother-to-child transmission by maternal HBeAg serostatus and the risk of becoming a chronic carrier following infection in newborns.
The boundary conditions for the differential equations describe the number of male and female births at each timestep, which were calculated by multiplying the age-specific fertility rates with the number of women of reproductive age (age 15-49 years) in each compartment, and applying the sex ratio at birth. This is calculated as: Where (0) is the risk of becoming a chronic carrier at age 0, is the probability of motherto-child transmission from a HBsAg-positive mother depending on maternal HBeAg or treatment status ( for HBeAg-positive mother, for HBeAg-negative mother and for treated mother), and:

Natural history of chronic HBV infection
The full model structure is shown in Figure S2 Stratification based on the EASL clinical model was used in a previous global HBV modelling study [3] and was also considered the most suitable mechanistic approach for the purpose of this study, because: • Results from the scoping review and more recent literature showed that the clinical risk factors for liver disease underlying the compartments have been confirmed in sub-Saharan African populations (e.g. HBeAg, high viral load, elevated ALT) [8,63].
• Adoption of the EASL infection stages in the model structure allowed to easily apply the EASL HBV treatment criteria, which are currently the most commonly used reference criteria in sub-Saharan African studies [64].
• In the absence of an African-specific clinical model of HBV infection, the highest-quality data on disease progression to date is based on the EASL classification [8].  to one of the infection states at any one time, and that classification into these will usually require measuring the different clinical markers at several timepoints [8].

Age-and sex-specific natural history transitions
Age-or sex-dependent transitions between model compartments in the model are detailed below. Similar assumptions on disease progression rates have been applied in previous mathematical models [3,20], and the mechanism behind many of these, including identification of age and sex as risk factors for disease progression, are well-established [65].
However, based on evidence from the scoping review, the age-and sex-dependence of some progression rates were adapted to the sub-Saharan African context. Equations use the following nomenclature: r represents a fixed rate (described by a single value), f represents a function (a rate depending on another factor, usually age a or sex g), m represents a multiplier (usually a rate ratio) and c represents a coefficient in function.

Age-dependent risk of becoming a chronic carrier after acute infection
A key determinant of different epidemiological patterns of HBV across the world is the agespecific risk of progressing to chronic carriage following acute infection [66], which is highest in the youngest age groups. As described in Edmunds et al. 1993 and [1, 20], the risk of developing chronic carriage was represented using an exponential decay function of age at infection for those aged 6 months and over, but was assumed to be higher for infants infected at less than 6 months of age through vertical transmission. This is This function was introduced to reflect the observations in a Gambian cohort of the crude rate of HBeAg loss increasing with age [8], and is consistent with previous evidence that the duration of the HBeAg-positive infection phase seems to be shorter in chronic infections acquired in adulthood compared to childhood [67,68]. Nevertheless, the option of progression through the HBeAg-positive compartments remaining constant over age is also inferred in the calibration through the parameter, whose prior distribution includes 0.

Age-dependent rate of HBsAg loss
The age-specific rate of HBsAg seroclearance, → ( ), corresponding to the transition from the HBeAg-negative infection to the Recovered/Immune compartment, was described as a linear function of increase with age, as informed by the slope coefficient: This was based on analysis of age-specific HBsAg loss rates data from Shimakawa et al. [8], which showed a significant linear association between current age and the rate of HBsAg loss after adjusting for sex, calendar year and birthplace.

Age-and sex-dependent progression to compensated cirrhosis
A general feature of chronic HBV infection is HBeAg positivity early in the infection, which is usually lost as the infection progresses, giving rise to the age-specific pattern of HBeAg prevalence. However, if HBeAg persists, it was found to be a risk factor for progression to liver disease in older carrier cohorts [8]. In the model, the progression rate from HBeAg-positive CHB to compensated cirrhosis, → ( ), was assumed to be constant with age above the age threshold, , below which no development of cirrhosis occurs: This allows for the distinction of the effect of HBeAg positivity on disease progression based on duration of infection.
The higher risk of cirrhosis in men was represented through calibration of , the rate ratio for progression from CHB to compensated cirrhosis in men compared to women. This parameter also governs the sex-dependent progression from HBeAg-negative CHB to compensated cirrhosis, → ( ), by multiplication with the corresponding progression rate in women, → :

Age-and sex-dependent progression to HCC
Progression to HCC in the model occurs at different rates from all chronic carrier compartments. An age threshold ℎ , below which no progression to HCC occurs, was introduced to regulate age-specific progression to HCC as this outcome is rare in children.
Progression to HCC strongly increases with age [49], therefore these progression rates from all chronic carrier compartments except for decompensated cirrhosis were described using the same shifted quadratic function: The baseline age-specific HCC incidence rate in women in the HBeAg-negative infection phase, ℎ , was calibrated and rate ratios were applied to this for progression to HCC from the other compartments ( → parameters) and from men in the respective compartments ( ℎ parameter).
HBV viral load has been established as an important risk factor for HCC in the Taiwanese REVEAL cohort, and underlying liver disease is known to increase the rate of progressing to HCC in chronic carriers [43]. For this reason, the rate of developing HCC was assumed to be lowest in HBeAg-negative infection, followed by HBeAg-positive infection, HBeAg-negative CHB, HBeAg-positive CHB and compensated cirrhosis. The rate of progression to HCC from decompensated cirrhosis is assumed to be constant with age.

Assumptions on the effect of sex in natural history
The increased risk of developing liver disease, including HCC, in men compared to women, was reflected in several progression rates in the model [3,43]. As shown above, a multiplier for men was applied to the rates of progression to compensated cirrhosis from HBeAg-positive and HBeAg-negative CHB ( ) and to HCC from all chronic carrier compartments except for decompensated cirrhosis ( ℎ ). The rate ratio was assumed to be potentially different for progression to compensated cirrhosis and for progression to HCC, due to the distinction between the liver disease pathway and the viral DNA integration pathway to HCC and the hypotheses for the reasons underlying the sex differences [30].

African context
Several environmental, genetic or lifestyle risk factors for increased risk of disease among chronic HBV carriers have been described or hypothesised, for example coinfections with HIV, hepatitis delta or hepatitis C virus, aflatoxin exposure and HBV genotype [6,8,69,70].
However, since the purpose of this study was to represent the general chronic HBV carrier population in The Gambia, as a case study of chronic carriers in sub-Saharan Africa more generally, these risk groups were not explicitly represented in the model structure. Instead, progression rates calibrated based largely on West African data implicitly include the prevalence and distribution of these risk factors in the study population at the time of data collection. This focus on West African data may affect generalisability of the results to other African countries, as distribution of some risk factors varies across the region.

Implemented interventions: infant vaccination
Routine infant vaccination was modelled as conferring all-or-nothing lifelong immunity from chronic HBV infection by removing infants from the susceptible compartment at a rate ( , ).
The age-and time-dependent annual vaccination rate ( , ) is defined as: vaccination. This assumes that vaccination with less than 3 doses confers no immunity. A logarithmic adjustment was applied to convert the effective vaccine coverage into a transition rate [71], accounting for the observation that the vaccination schedule is usually completed within the first 6 months of life in The Gambia [28]. Given high estimates of vaccine efficacy, the proportion of 1-year old children immune to HBV as a result of vaccination in the model was confirmed to be almost as high as the observed WHO coverage data at 1 year of age.

Simulated interventions: antiviral treatment Treatment regimens and eligibility
The treatment regimen implemented in the model consists of first-line oral antiviral nucleos(t)ide analogues, in particular tenofovir disoproxil fumarate. Both entecavir and TDF are widely used worldwide due to their high efficacy, favourable safety profile, and ease of administration and patient management compared to older treatment regimens like lamivudine and interferon [72]. Entecavir has been shown to have very similar efficacy to TDF [73] and both drugs are off patent [74]. Nevertheless, as TDF is already used in most of Africa in HIV treatment regimens [75], this was considered to be the most likely HBV antiviral therapy to be scalable in the sub-Saharan African context.
The recommended treatment duration with TDF is indefinite in nearly all patients, therefore lifelong antiviral therapy was assumed in the model. Due to the excellent safety profile of TDF and high barrier to resistance [22], potential side effects of treatment or treatment failure as a result of drug resistance were not accounted for.
According to EASL 2017 guidelines, carriers in the HBeAg-positive CHB, HBeAg-negative CHB, compensated and decompensated cirrhosis states, as well as carriers over the age of 30 years in the HBeAg-positive infection phase, were eligible for treatment [22]. Carriers in the HBeAg-negative infection phase usually have a very good prognosis and minimal liver damage, and are therefore not considered in need of antiviral treatment. EASL treatment criteria were chosen over those from WHO because they are currently the most common reference criteria used in published African treatment studies, and are in agreement with the clinical guidelines developed by other international liver associations [15,64,76]. Evidence from studies of treatment eligibility in sub-Saharan African populations also suggests that the WHO guidelines, developed specifically for use in resource-limited settings, fail to identify a substantial proportion of patients in need of treatment from a clinical perspective, especially those who would benefit most from a timely initiation to prevent advanced disease [76].

Development of the treatment model structure
The treatment model structure for treatment-naïve HBV carriers was developed and parameterised based on the most recent international evidence on disease progression on antiviral therapy, as only little data was available from a sub-Saharan African setting at the time of development.
Long-term treatment with nucleos(t)ide analogues is highly effective in suppressing HBV viral load, normalising biochemical response, and halting or reversing the progression of liver damage and cirrhosis, but does not prevent the development of HCC [72]. Therefore, disease progression on treatment was captured within 6 compartments, corresponding to 4 different treated disease stages and 2 possible long-term outcomes on treatment (Figure S2.5).
Movement into the treated compartments represents effective viral suppression, which has been widely reported to occur in almost all patients within a short time on treatment [72,77], including in sub-Saharan African populations [15,75,78]. For simplicity, we therefore assumed viral suppression occurs in all patients initiating treatment within one timestep of 6 months in the model. This means that treatment has an immediate effect on liver disease progression in all patients upon initiation.

Assumptions on outcomes of treated carriers
Outcomes on treatment in the model vary by the disease state at treatment initiation. Carriers In addition to histological improvement and preventing the progression to cirrhosis, studies have shown that antiviral therapy can lead to regression of cirrhosis in the majority of patients [80]. However, the implications of this for future disease progression to HCC are uncertain. In the model, we therefore assumed no disease regression to other compartments on treatment, though reduced HCC risk experienced by the treated persons may in part be due to histological improvement [60]. Instead, antiviral therapy was assumed to be 100% effective at halting progression to cirrhosis if it is initiated before the onset of cirrhosis, as well as no further decompensation of cirrhosis on treatment [81]. We also assumed a reduction in cirrhosis mortality rates on treatment to reflect the slowed progression of liver disease and an improvement in complications in decompensated cirrhosis patients [22].
Due to viral integration in the host liver cell genome and persistence of covalently closed circular DNA, a reduced risk of progression to HCC remains even while on treatment, which is higher in patients with underlying cirrhosis at treatment initiation [82][83][84]. The age-and sexdependency in progression rates to HCC also appears to be maintained on treatment [60,83].
In the treatment model, the calibrated untreated progression rates from all compartments to HCC were reduced according to the hazard ratios from the international literature, thereby assuming that the effect of treatment is the same in sub-Saharan African carriers in a given infection or disease state as estimated in studies in other populations, and also allowing to maintain the increased risk of HCC in cirrhotic compared to non-cirrhotic carriers. Though little evidence on varying effects of first-line treatment regimens by genotype or ethnicity is available to date, a comparison of Asian and non-Asian (predominantly Caucasians with genotypes A or D) participants in TDF trials found similar levels of viral suppression, ALT normalisation and histological improvements achieved in these two groups [85].
Based on a retrospective cohort study in North American and Taiwanese patients [60], we assumed a fixed reduction of progression to HCC with treatment of 73% for CHB and 77% for cirrhotic compartments. This study was chosen based on treatment regimen, long-term followup, and incidence rates being in line with those reported in other large studies [84]. However, estimates of hazard ratios vary across studies to some degree, particularly regarding differential treatment effect by cirrhotic status [86], which was therefore further explored in sensitivity analyses.
As the treated HCC compartment represents development of HCC following treatment and other therapeutic options for management of HCC such as liver transplants are not widely available in sub-Saharan Africa, we assumed no change in the mortality rate from HCC with treatment.

Treatment of carriers in the HBeAg-positive chronic infection phase if aged over 30 years is a
new conditional recommendation in the 2017 version of the EASL guidelines and accordingly used in the current treatment of HBV carriers in ongoing studies [87]. However, evidence on disease progression following treatment in these patients is lacking. Although a Korean study suggested a similar reduction in progression to HCC in treated HBeAg-positive infection as we assumed for CHB (adjusted hazard ratio of 0.19, 95% CI 0.05-0.69) [59], treatment need in these patients remains controversial [88,89]. On the population level, this was thought not to have a substantial effect on projections of treatment impact due to the small number of HBV carriers remaining in this phase over the age of 30 years in sub-Saharan Africa [8].
Serological recovery through HBsAg seroclearance is considered the ideal end point of antiviral therapy, but represents a rare outcome. In a recent systematic review and metaanalysis, rates of HBsAg seroclearance were estimated to be similar on treatment as in untreated carriers, and not associated with genotype [90]. As a result, the same age-specific rate of HBsAg loss as in untreated carriers was applied to the treated CHB compartment, which was also consistent with new data from a treated cohort in Ethiopia [61].

Assumptions on treatment adherence and duration
We modelled all patients initiating treatment to remain on the recommended life-long antiviral therapy course, expect for treated CHB carriers experiencing HBsAg loss. Imperfect adherence or cessation of therapy was not explicitly accounted for in the model. Though lifelong perfect adherence to treatment is unlikely to be realistic in practice, evidence on disease progression after stopping of nucleos(t)ide analogue therapy is inconclusive and potential options for discontinuation are an active area of ongoing research. Discontinuation is considered safe and recommended in the small proportions of patients achieving HBsAg loss, and can be considered as an individualised option in HBeAg-positive non-cirrhotic patients after HBeAg seroconversion and consolidation therapy [22,91]. In recent years, sustained virological suppression has been observed in HBeAg-negative patients without cirrhosis following discontinuation after long-term treatment, although these patients still require close post-treatment monitoring to detect relapse [92,93]. Interestingly, these results also suggest that stopping of nucleos(t)ide analogue therapy may increase the chance of HBsAg seroclearance. Nevertheless, in many other patients, treatment discontinuation appears to lead to ALT elevations within a short time [94], as well as increased disease progression such as to liver decompensation [95].
Conversely, current clinical trials have only followed treated patients for a maximum of around 10 years, so longer-term effects of treatment are also not known. Recent evidence suggests that the rate of progression to HCC declines with a longer treatment course in cirrhotic patients [84], so any potential longer-term benefits of lifelong therapy may not be reflected in the current data and thereby the parameter values in the model. Similarly, though imperfect adherence to treatment was not modelled explicitly, it may be implicitly represented in the parameters governing treatment efficacy, as the progression rates to HCC on treatment represent the average progression of a cohort treated and followed-up for a study period of 8 years. The treatment initiation uptake parameter can also either be interpreted as individuals not initiating treatment or not adhering to treatment enough for a beneficial effect on disease progression to occur.

Assumptions on infectivity of treated carriers
Reductions in infectivity of HBV carriers due to treatment are difficult to measure. Since nucleos(t)ide analogue therapy effectively suppresses HBV replication to undetectable levels, comparable to those in over half of treatment-ineligible inactive carriers in the HBeAg-negative chronic infection compartment [15], we assumed all treated carriers irrespective of HBeAg status at treatment initiation to be as infectious as HBeAg-negative untreated carriers in the model. We assumed this relative infectiousness for both horizontal transmission (governed by the parameter) and for treatment among pregnant women and their risk of MTCT ( parameter). In the modelled scenarios, the latter applies to pregnant women receiving longterm antiviral therapy for prevention of individual disease progression and does not represent the MTCT risk for women receiving peripartum antiviral prophylaxis for the purpose of preventing MTCT.
Indirect evidence from a meta-analysis of prevention of MTCT with antiviral treatment during pregnancy appears to confirm that treatment has a significant impact on reducing infectivity, at least in the highly viraemic mothers who would be eligible for peripartum antiviral prophylaxis [96]. Though peripartum nucleos(t)ide analogue therapy is offered in conjunction with birth dose vaccination and HBIG in all studies, rates of failure to prevent MTCT were estimated at around 23% if only the birth dose vaccine and HBIG were given, but significantly lower at 6-11% if pregnant women additionally received peripartum antiviral prophylaxis. This is also consistent with their estimate of a 78% reduction in maternal viral load with peripartum antiviral prophylaxis [96]. Nevertheless, given the large uncertainty in how this might translate to infectivity in a treated population, a sensitivity analysis assuming no possibility of transmission from treated HBV carriers was also conducted.

Modelling of the mass screening and treatment intervention and the treatment cascade
A simplified cascade of care for clinical management of HBV was implemented in the model.
In the modelled intervention, two potential routes to antiviral therapy are represented according to international guidelines: a) the initial mass screening intervention using HBsAg testing and clinical assessment to identify chronic HBV carriers in need of treatment in the population, and b) regular clinical monitoring of those carriers engaged in care who were found to be not eligible for treatment at the initial assessment.
The treatment cascade is described by parameters for the screening coverage in the targeted population, , the proportion of diagnosed HBV carriers undergoing full clinical assessment for treatment eligibility, , the proportion of HBV carriers identified as treatment-eligible who initiate antiviral therapy, , and the proportion of HBV carriers identified as treatment-ineligible at initial assessment who complete the monitoring assessment at each follow-up, (Figure S2.6).

Figure S2.6. Diagram of the simplified treatment cascade for hepatitis B.
The cascade is represented using model parameters for screening coverage ( ), clinical assessment uptake ( ), treatment uptake ( ) and monitoring uptake ( ). Diagnosed HBV carriers are a subset of the total tested population.

Mass screening and treatment programme
Hypothetical screening and treatment in the general population was modelled as a mass intervention programme which instantaneously moves a given proportion of the targeted population into the Diagnosed (untreated) and Treated compartments. Specifically, upon HBsAg testing, a proportion of undiagnosed treatment-eligible HBV carriers are moved to the corresponding treated compartment, and a proportion of undiagnosed treatment-ineligible carriers are moved to the corresponding diagnosed compartment (section Equations for the mass screening and treatment programme). This approach assumes that screening, clinical assessment and treatment initiation of the targeted population occurs within a short time interval of 6 months. In the code, it was implemented by triggering an "event" in the deSolve package that instantaneously changes the values of the respective state variables. Screening coverage is applied randomly to the targeted population, such as the general population falling into a given age range.

Monitoring of HBV carriers ineligible for treatment at initial assessment
European and other international guidelines recommend regular follow-up of at least once a year of HBV carriers not meeting treatment criteria at first assessment [22,65,97]. Monitoring for disease progression to treatment eligibility among the diagnosed initially treatmentineligible carriers is modelled as a continuous process, so that monitoring in treatment-eligible compartments leads to treatment initiation into the corresponding treated compartment at a constant rate ( ): In this equation, ( ) is the average time interval between monitoring assessments, which is varied in scenario-based analyses and can vary by age. is the probability of monitoring uptake and is the probability of identified treatment-eligible carriers initiating therapy. The treatment rate among those being monitoring, , does not depend on sex and is equally applied to the diagnosed CHB, cirrhosis and decompensated cirrhosis compartments.
For diagnosed carriers in the HBeAg-positive infection state, the rate of treatment among those being monitored, → ( ), is only applied to over-30 year olds according to treatment criteria [22].
Since monitoring occurs at a constant rate in the model, an average monitoring interval ( ( )) of e.g. 5 years translates to 20% of the population in the given compartment being monitored and initiated on treatment each year, and everyone having been monitored once after 5 years, twice after 10 years, etc. The treatment rate is reduced if not all carriers attend the monitoring assessments or initiate treatment where necessary ( or < 1).

Further assumptions about the treatment cascade
The equations in previous sections only describe movements between compartments.
However, to calculate the total population to screen, assess for treatment eligibility and initiate on treatment as a model outcome, the respective coverage parameters were applied to the whole population, all diagnosed chronic carriers and all identified treatment-eligible carriers, respectively. Similarly, monitoring events were counted among all diagnosed compartments.
All parameters describing the cascade of care were assumed not to vary based on disease status, age or sex. All tests and clinical assessments were assumed to have perfect sensitivity and specificity in diagnosing chronic HBV infection and identifying the clinical stage of disease governing treatment eligibility.

Discussion of influence of assumptions in treatment model on results
Conclusions about cost-effectiveness could be affected by the model assumption of perfect lifelong adherence to antiviral therapy. The feasibility of this is a key consideration for the projections of high treatment impact in young carriers, as the effect of including 15-30 year olds in a screening programme now compared to screening the same cohort at a later time was not compared. Globally, adherence to antiviral therapy for HBV was estimated at 75% [98], but evidence on the impact of treatment discontinuation on disease outcomes was considered too inconclusive to allow exploration in the model at present [91].
Other structural assumptions in the treatment model are likely to affect conclusions about the treatment programme, for example that the benefit of treatment does not vary by age independent of disease state or over time, that treatment leads to immediate viral suppression and that treated carriers experience a constant rate of developing HCC over their lifetime.
Given the large benefits associated with the initial assessment alone, lack of retention of treatment-ineligible carriers in monitoring did not affect the cost-effectiveness of a treatment programme without monitoring as it also saves resources for assessing those individuals lost to follow-up over time (see Sensitivity analysis of cost-effectiveness results). However, dropout of carriers to monitor over time was not modelled explicitly, but was represented as an average 80% attendance at each monitoring visit. If in reality the drop-out rate was high early on, the model may overestimate identification of disease progression by monitoring and thereby its impact. We also did not explore the option of potentially differential drop-out rates with longer versus shorter monitoring intervals, which could make more frequent monitoring frequencies more cost-effective. However, it is noteworthy that given the modelled age distribution of chronic carriers, a monitoring strategy of every 5 years in 15-45 year olds would involve an average of less than two follow-up visits per person in total.

C. Model calibration Approach
The model was calibrated in a Bayesian framework to synthesise epidemiological evidence from many different sources, and to allow quantification and propagation of uncertainty in input parameters. Results from the scoping review informed the choice of priors, calibration targets and which parameters to vary in the calibration.
A rejection-sampling Approximate Bayesian computation (ABC) algorithm was used for the calibration [99]. 1 million Latin Hypercube samples were drawn from the defined prior parameter space. The model outputs simulated from these parameter sets were compared with the empirical epidemiological data using a distance function, and the sample of parameter sets with a distance falling below a defined tolerance level were accepted.

Prior distributions
All parameters of the model representing the current epidemiology in The Gambia (without treatment) were varied in the calibration procedure across a range of prior probabilities (Table   S2.4). This choice was made because most of the available sub-Saharan African data informed modelled outcomes that are functions of several parameters, instead of allowing to update individual parameters directly.
A total of 21 datapoints from 11 studies were identified for parameterisation, only four of which were longitudinal measurements matching natural history transitions or HBV-related mortality in the model (not shown). For most parameters, for which no data from sub-Saharan Africa was identified, priors were informed by evidence from other geographical areas and expert opinion, but were specified to be less informative by increasing the spread, both to account for the general uncertainty in the measurements as well as their applicability in sub-Saharan African populations. The most informative prior distributions were specified for wellestablished parameters such as infant vaccine efficacy and the rate ratios for progression to cirrhosis and HCC in men compared to women (Table S2.4). The centre and range of prior distributions was derived from the data sources reviewed for a previous modelling study [36] and more recent systematic reviews. Where available, multiple sources were considered to determine averages and ranges of the prior distributions.
Prior distributions for the individual inputs in composite parameters (usually of the age-and sex-dependent transition rates) that are not observed directly were derived by adjusting empirical measurements from studies set in specific populations using the progression functions described above.

ABC algorithm
The steps in rejection-sampling ABC [100], with the aim of minimising the error between simulated and observed data, are: 1. Sample a set of parameters * from their prior distribution ( ).
2. Generate the simulated data * from the model. 3. Compare the simulated output, * , with the observed data, , using a distance function and tolerance level ϵ.
Thereby, the rejection algorithm rejects all but the N parameter values that generate model outputs closest to the calibration targets, which form a sample from an approximation of the posterior distribution [101]. The algorithm was stopped after having sampled the pre-specified 1 million prior parameter sets.
To compute the observed outcomes, which depend on clinical and demographic population characteristics, populations similar to the respective study populations were simulated, and measured outcomes that were not explicitly represented in the model structure were approximated. Full details of how empirical observations were linked to pathways in the model are detailed in Table S2.7.
The distance between individual observed datapoints and corresponding model outputs was summarised in a single summary error value across all calibration targets, ( , ). The weighted sum of relative squares (SSE) was chosen as the union metric and calculated as: where i refers to the individual calibration datapoints, with si being the simulated value and sobs,i the empirical value, m is the total number of calibration targets, and is the assigned datapoint-specific quality-based weight.
This distance metric was chosen to reflect key properties of the dataset in question, namely the varying scales of the different datapoints, and the existence of potential (unknown) contradictions and outliers. It allowed to prioritise achieving a good overall fit over capturing all patterns in the data equally well [102], and allowed to make use of all the available data of varying quality. The evidence on HBV natural history processes embedded in the model structure, in combination with quality-based weights on the calibration targets, determined the prioritisation of some datapoints over others. Weights were assigned based on quality scores reflecting subjective confidence in the different data sources, as further detailed in the Data sources used to inform model parameters through calibration section.
The choice of tolerance level aims to achieve a balance between accuracy of the posterior approximation and a computationally feasible acceptance rate [103]. For the dataset in question, where the decision of how close the simulated data should be to the observed data was not straightforward, we used a two-step approach to determine an appropriate tolerance level. Firstly, a broad target range was applied to the final simulations of HBsAg prevalence to ensure a realistic endemicity level among all accepted simulations. Parameter sets were sorted by their SSE and a cut-off applied to discard all simulations with a HBsAg prevalence outside the 1.3-41% range in over-20-year-olds, based on the minimum and maximum confidence interval bounds in the calibration dataset. Secondly, for the remaining 9,808 lowest-SSE parameter sets, we adopted the approach described in a previous study whereby the final tolerance level is chosen so as to maximise the precision in approximate posterior estimates [104]. K-means clustering was applied to the previously accepted parameter sets to find the tolerance level giving the smallest interquartile range across all posterior parameter values. This led to the final selection of the 183 lowest-SSE parameter sets, corresponding to a tolerance level of =76.25 and an acceptance rate of around 0.02%.

Propagation of uncertainty
Forward projections were made using the 183 accepted parameter sets to propagate the uncertainty in calibrated parameter values to the outcomes of interest in the analysis.
Uncertainty in model outputs was quantified by reporting the median and 95% equal-tailed credible interval (CrI) (2.5 th and 97.5 th percentiles) of projections. Note that the uncertainty around projections only represents the uncertainty in epidemiological parameters relating to transmission, vaccination and untreated natural history. Uncertainty bounds on modelled outcomes do not account for the uncertainty in demographic projections or the effect of treatment on disease progression.

Data sources used to inform model parameters through calibration
The model was calibrated to 345 epidemiological datapoints from 38 papers, shown in Table   S1. This included primary data and modelled estimates derived from systematic reviews and modelling studies, identified in the first stage of the scoping review. The primary data used as calibration targets broadly fall into the following categories: seromarker prevalence, transmission, disease progression in chronic HBV carriers, disease progression in liver disease patients, risk factors for liver disease in chronic HBV carriers, cross-sectional characteristics of chronic HBV carriers, and cross-sectional characteristics of liver disease patients. Assumptions made in inclusion, processing and modelling of the different types of extracted calibration data are detailed in Table S2.7.
The weighting scheme was adapted empirically over several rounds of calibration. Previous attempts at a more neutral approach giving equal or similar weights across datapoints led to overrepresentation of late-stage disease among calibration targets. This is not representative of disease progression among chronic carriers on average, as many hospital-based studies reflect patient characteristics at presentation rather than at onset. This led to acknowledgement of the low to moderate quality of the majority of the datapoints in subsequent approaches by numerically differentiating calibration targets more strongly based on data quality, and by assigning a low weight to most targets. The default weight was 0.1, which was increased to 1 only for data from good-quality studies representative of the general population. An additional purpose of the weighting scheme was to reconcile conflicts in data on the same outcome from multiple sources. In these cases, the calibration targets were differentiated by up-weighting only the highest-quality studies. For seromarker prevalence studies, quality was assessed based on a combination of sample size, representativeness of the study population, geographic scope and quality of information on the age group under study. Additionally, only individual calibration targets on cross-sectional characteristics of chronic HBV carriers, the age-specific risk of developing chronic infection, and MTCT risk were upweighted. In general, low weights were assigned based on methodological issues in the original study (most commonly very small sample sizes or bias in ascertainment of liver disease, as informed by expert opinion), or difficulty in approximating the outcome in the model. Priority was given to datapoints describing the general population of chronic HBV carriers.

Type of data Details and assumptions Use in model Seromarker prevalence
The model was calibrated to three population-based measures of relevant seromarkers in The Gambia: HBsAg prevalence, representing current chronic infection, anti-HBc prevalence, representing exposure to HBV or the proportion of the population who has ever been infected (either current infection or serological recovery), and HBeAg prevalence in chronic HBV carriers, representing increased infectivity. Only anti-HBc prevalence data from the pre-vaccination period was included as (anti-HBc-negative) vaccine-induced immunity was not distinguished from (anti-HBc-positive) infection-induced immunity in the model structure.
HBsAg seroprevalence data was not searched for systematically, but was extracted from the studies included for other reasons and complemented by data from studies in a WHO systematic review [5,105]. HBsAg prevalence was included if it was deemed representative of national HBsAg prevalence in The Gambian population; prevalence in study participants sampled based on their vaccination status in the Gambia Hepatitis Intervention Study or the Keneba-Manduar vaccination pilot was excluded. Vaccine effects on prevalence observed in the Keneba-Manduar trial was extrapolated to the national level by adjusting the time since vaccine introduction (from 1984 to 1990).
Seromarker prevalence was calibrated by stratifying by age and sex where relevant. The model output was calculated in the age group matching the average age of the respective study population, using the following equations: HBsAg prevalence in the general population

HBV infection incidence
Data on the incidence of HBV infection in the population was only included from studies set in The Gambia, as this depends on background endemicity levels. Infection incidence in children by maternal HBsAg status was only included if stratified according to age younger or older than 1 year, to allow differentiation between MTCT and horizontal infection. In young age groups, progression from seromarker-negative status to anti-HBs positivity was interpreted to represent acquisition of acute infection followed by serological recovery.
Rates of infection with HBV in the population were calculated as described for disease progression rates (see below).

Transmission: Mother-to-child
Estimates of the risk of vertical transmission with unknown maternal HBeAg status were included as calibration targets, if the ascertainment of Data of overall MTCT risk were calibrated by calculating the proportion of all babies born to HBsAg-positive 53

Type of data Details and assumptions Use in model transmission risk in HBsAg-positive women
MTCT met the definition of HBV infection detected through HBsAg or HBV DNA within the first 3-12 months of life of an infant born to an HBsAgpositive mother. As in the systematic review informing the priors on MTCT risk by maternal HBeAg status [2], it was assumed that all HBV infections in under 1 year olds born to HBsAg-positive mothers are due to MTCT, and all new infections occurring after the first year of life representing horizontal transmission events. mothers who are born as a chronic HBV carrier (born into the HBeAg-positive infection compartment) in the year of data collection of the given study. The overall MTCT risk was averaged between births from HBeAgpositive and HBeAg-negative women of childbearing age.

Transmission: Age-specific risk of becoming a chronic carrier following acute HBV infection
Data sources on the age-specific risk of developing chronic infection were derived from Edmunds et al. 1993 [1], as no additional studies on this were identified in the scoping review. However, as the original study included data from different world regions, the function of chronic carriage risk was fitted only to the West African datapoints of the proportion of children having progressed to chronic carriage following acute infection at various ages at infection.
In extracting the data, the methodology described in Edmunds et al. 1993 was applied. The age at infection in a study, if not reported, was assumed to be the mean or mid-point of the sample's age group. Development of chronic carriage was defined as a persistence of HBsAg seropositivity over at least 6 months, or progression from HBsAg or anti-HBc seropositivity to HBsAg seropositivity at least 6 months later.

Disease progression in chronic HBV carriers and liver disease patients
Extracted longitudinal data informing the natural history of chronic HBV infection or liver disease in West Africa included disease progression risks, rates and Kaplan-Meier survival curves, with long-term follow-up of a chronic HBV carrier cohort in The Gambia representing the most recent and highest-quality African evidence on this to date [8]. Progression rates from Mendy et al. 2008 [106] were excluded as these relate to the same participants as the subsequent follow-up analysis. In studies where longitudinal outcomes were presented as the risk of the outcome over an average follow-up period or the mean time to the outcome, they were converted into rates per person-year using the following standard statistical equations, under the assumption that the rate of the event is constant over time [16]: To capture the age-, sex-and time-dependent processes in the natural history of chronic HBV infection or isolate a subset of transitions in the model, calibration to some datapoints required simulation of specific cohorts of chronic carriers with known baseline age and infection status to replicate the characteristics of the original study population and thereby the calibration targets. Progression rates were calculated as the cumulative number of events of interest over the follow-up duration in the model, divided by the personyears spent in the compartments at risk. As in the corresponding cohort studies, compartments at risk were those containing individuals at risk of potentially developing the outcome of interest in the model (directly or indirectly). Person-years at risk were calculated as the sum of individuals in the respective compartments at each timepoint over the follow-up 54

Type of data Details and assumptions Use in model
The cumulative probability of the outcomes of interest over time was extracted from Kaplan Meier survival curves and used directly as calibration targets. A survival curve for cirrhotic patients was additionally calculated from the deaths data in Diarra et al. 2010 using the life-table method [107].
period, multiplied by the timestep dt. Rates were stratified by age and sex where the data suggested relevant differences. The cumulative probability of mortality (or other event) extracted from survival curves was calculated as the total incident deaths or events at a given timestep since entry into the cohort, divided by the population at risk at entry.

Risk factors for liver disease in chronic HBV carriers
All measures of association for clinical or demographic characteristics with development of liver disease in chronic carriers were extracted from the literature. Other identified odds ratios that could not be approximated as processes in the model were not included. Much evidence on risk factors for liver disease came from the Gambia Liver Cancer Study [42,69,108], of which only the paper with the most rigorous statistical analysis and the largest sample size was included [109].
Odds ratios were calculated in a given age group, sex and at a given timestep according to the standard epidemiological definition, by deriving the number of exposed and unexposed cases and controls.

Cross-sectional characteristics of chronic HBV carriers and liver disease patients
The majority of datapoints on characteristics of chronic HBV carriers or liver disease patients described the prevalence of different disease states. The extracted estimates highlight that it is often not possible to assign chronic carriers to a specific phase of chronic infection with a single crosssectional measurement of different variables; for example, in the Gambian cohort at baseline almost 20% of study participants were unclassified [8]. These unclassified carriers were excluded in the calibration targets by removing them from the denominator. Additionally, the data on distribution of disease states does not correspond directly to the criteria for treatment eligibility, which required a more stringent ascertainment including a liver disease assessment.
Characteristics of chronic HBV carriers and liver disease patients were calculated as the cross-sectional proportion of individuals in a set of compartments, in a given age group, sex and timepoint.

External model estimates of disease burden: HBV-related HCC incidence and mortality
Age-and sex-specific estimates of country-specific liver cancer incidence and mortality in The Gambia were available from the GLOBOCAN database for the years 1988, 1998 and 2018. All liver cancer cases were assumed to represent HCC, as these are the most common [110]. HCC incidence estimated by GLOBOCAN at the International Agency for Research on Cancer is based on data from the National Cancer Registry of The Gambia [10], a population-based registry established in 1986 to collect data allowing to estimate the impact of HBV vaccination on liver cancer in the Gambia Hepatitis Intervention Study [111]. As estimates from GLOBOCAN represent population-wide HCC cases and deaths of any aetiology, these calibration targets were multiplied by The modelled age-and sex-specific incidence of HCC and mortality from cirrhosis in different years was calibrated according to the definition of the annual incidence rate in GLOBOCAN, using the total population size at the given year mid-point as the denominator. The numerator for the population-based cirrhosis mortality and HCC incidence rates were the number of additional HBV-related deaths from the compensated and decompensated cirrhosis compartments and the number of incident HCC cases from all chronic carrier compartments in the given year, 55 Type of data Details and assumptions Use in model the population attributable fraction of HCC attributable to chronic HBV infection. In the scoping review, no longitudinal studies allowing to estimate the PAF were identified. Case-control studies were included if HCC or cirrhosis patients were recruited as cases, controls were individuals without chronic liver disease, and the exposure was a positive HBsAg test. Two Gambian studies, including the Gambia Liver Cancer Study, were identified providing data for this. Odds ratios from these studies were used to estimate the PAF using the standard epidemiological formula [112]: Where ( ) is the prevalence of HBsAg among HCC patients.
Based on this data, 57% of HCC was estimated to be attributable to HBsAg [42,113]. The PAF for HBV-related HCC was assumed to be constant by age, sex and over time. Though some of the studies identified in the scoping review suggested a lower HBsAg prevalence and odds ratio in older HCC patients [42,113], the sample size of the latter study was small and it was unclear how this would translate to the age-specific HBVrelated HCC incidence rates. Previous meta-analyses on the PAF of liver cancer due to HBV also did not present differences by age [114,115].
respectively. These rates were calculated across the specified age range

External model estimates of disease burden: HBV-related cirrhosis mortality
Age-and sex-specific estimates of cirrhosis mortality for the years 1990 and 2017 came from the Global Burden of Disease study. Global estimates of HBV-related cirrhosis mortality from GBD are based on data from vital registration and verbal autopsies, though the data sources for most sub-Saharan African countries were sparse [116]. No empirical data was available from The Gambia specifically and the data quality rating in the study was low, implying that these estimates are strongly determined by model covariates and regional patterns more generally. Cirrhosis mortality attributable to HBV was adopted from GBD directly, as their estimate of 49% in West Africa was almost identical to the Gambian data identified in the scoping review [69].

Model fits
This section shows the model fits for most of the calibration targets described above. Model projections were consistent with the majority of empirical data used in the calibration. Notable features include the reduction in chronic infection prevalence in the age groups covered by the routine vaccination programme and other transmission patterns (Figure S2.7), early loss of HBeAg with age and the majority of adult chronic carriers having HBeAg-negative infection ( Figure S2.8), the mortality experience of HCC patients (Figure S2.9), and age and sex patterns in hepatocellular carcinoma incidence (Figure S2.10), with a relatively young average age at onset of cirrhosis and HCC (Table S2.     Country-specific liver cancer rates from GLOBOCAN [10], based on data from the national cancer registry, were multiplied by the population attributable fraction to obtain rates for HCC attributable to HBV. Modelled estimates of rates of HBV-related cirrhosis mortality came from the Global Burden of Disease Study [116]. The model was additionally calibrated to data of HCC incidence in 1988 and 1998, and to cirrhosis mortality in 1990 from the same sources (not shown).  were similar to the prior distributions, suggesting that prior evidence agreed with much of the epidemiological data used in the calibration and that calibration targets did not provide sufficient additional information to reduce the uncertainty range of these parameters.
However, the calibration data allowed to update beliefs about several parameters, notably the progression rate from HBeAg-negative infection to HBeAg-negative CHB, the rate from HBeAg-positive infection to HBeAg-positive CHB, the age-dependent transmission coefficients (β1, β2, β3), the coefficient for progression to HCC in women, and the progression rate from HBeAg-positive CHB to HBeAg-negative infection. The parameters remaining most uncertain after calibration, in terms of having the largest posterior interquartile range relative to the median, were the minimum age for HCC, the progression rate from HBeAg-positive to HBeAg-negative CHB, the progression rate from HBeAg-negative CHB to compensated cirrhosis, and the coefficient for progression through the HBeAg-positive compartments.

Costing
All costs were estimated from a healthcare provider perspective in 2020 US dollars (US$).
Cost estimates from previous years and in different currencies were converted into US$ and adjusted for inflation using the Gambia gross domestic product (GDP) deflator rate [118]. Unit costs of these different components were applied to the resources utilised over time in the model, allowing to derive the total costs incurred in different scenarios. The cost of tenofovir and the rapid diagnostic test was derived from a previous global study [119]. Per-person programme costs of the screening intervention were assumed to be the same as in a community-based screening programme in The Gambia [36]. Laboratory cost data on the different diagnostic tests involved in clinical management of chronic HBV infection were collected locally, including the associated cost of human resources, upfront purchase and maintenance of diagnostic devices. Viral load testing is available at relatively low cost in The Gambia using an in-house PCR, but close to the GeneXpert costs estimated in a previous global study [119].
Our analysis was conducted from a health provider perspective, which does not account for labour productivity losses associated with premature deaths from HBV-related liver disease or the costs of end-of-life care provided by family members [36]. Additionally, potential nonlinearities between costs of diagnosis and treatment and their coverage levels were not taken into account for this study because estimating these economies of scale in the absence of implementation data is challenging, though reductions in unit costs would be likely if the intervention is scaled up to the high levels modelled in this study [120]. These assumptions could have led to an underestimation of the cost-effectiveness of the modelled strategies.
We also assumed that provision of the treatment programme would not save costs associated with management of cirrhosis or HCC because of the limited access to medical care for endstage liver disease in the public sector in most of sub-Saharan Africa [30]. A previous costeffectiveness analysis in The Gambia assumed that screening and treatment would avert some costs due to this, but varying hospitalisation costs for decompensated cirrhosis and HCC in sensitivity analyses had a negligible effect on the incremental cost-effectiveness ratio (ICER) of the screening and treatment programme in that study [36]. In our scoping review, we identified only few studies with data on the hospital costs of clinical management for cirrhosis and HCC in African countries, and the frequency of hospital admissions due to this in The Gambia could not reliably be determined. Comparison of the number of hospitalised patients identified in the country-wide Gambia Liver Cancer Study and a more recent study with estimates of HBV-related liver cancer incidence nevertheless gives an indication that this has been low historically [42,121]. It is therefore possible that provision of a screening and treatment programme could lead to increased identification, hospital admission and medical care for end-stage liver disease as well, especially since treatment does not fully prevent the development of HCC. Based on this limited data, we assumed that either costs incurred or saved through this would have relatively little effect on cost-effectiveness ratios in this study within uncertainty bounds, but this requires further data and consideration in future studies.    Among all parameters varied in the calibration, uncertainty in the incremental impact and costeffectiveness ratio (CER) of the treatment programme without monitoring, as well as of the 5yearly monitoring in <45-year-olds compared to no monitoring, was most associated with uncertainty in the progression rate from HBeAg-negative infection to HBeAg-negative CHB, and parameters relating to progression to, decompensation or mortality from cirrhosis (Table   S2.1). At the lower estimates of these parameters inferred in the calibration, the treatment programme with 5-yearly monitoring in <45-year-olds would not be considered cost-effective under the cost-effectiveness threshold of US$404 per DALY averted, whereas the treatment programme without monitoring had a CER below the estimated cost-effectiveness threshold under almost all calibrated parameter estimates. In one-way sensitivity analysis, projections of CERs for the same scenarios were robust to variations in parameters of treatment effect, and conclusions about the most effective costeffective strategy were not affected by varying reductions in HCC progression on treatment between 20-90% (Figure S3.3). However, assumptions about uptake at different stages of care had larger effects on CERs. Reductions in linkage to care and treatment initiation led to larger reductions in health impact than in costs due to the costs incurred at previous stages of care, and thereby increased the CER of the treatment programme without monitoring. Among coverage parameters, the largest increase in CER, up to US$409 (95% CrI 243-784) per DALY averted, occurred for a reduction of the proportion initiating treatment to 50%. With a reduced probability of linkage to care, the no monitoring strategy would be more strongly dominated by 5-yearly monitoring in <45-year-olds, while assumptions of lower screening coverage would result in both lower health impact and reduced total costs, thereby having only limited effect on ICERs (not shown).

C. Sensitivity analysis of cost-effectiveness results
Cost estimates at all stages of care had among the greatest effect on the cost-effectiveness of the screening and treatment programme overall, with CERs being most sensitive to an increased treatment cost within the assumed ranges, which includes the cost of tenofovir and annual monitoring (Figure S3.3). Conversely, the CER of the screening and treatment programme without monitoring and with 5-yearly monitoring in under 45-year-olds were most reduced by reductions in the cost of screening and monitoring, respectively.
Further comparison of the incremental cost-effectiveness ratios for all monitoring strategies under wide ranges of plausible cost estimates showed that at least one of the treatment strategies had a median ICER below current estimates of the cost-effectiveness threshold under all cost assumptions (Figure S3.4). Monitoring at any frequency would not be costeffective if both the initial and monitoring assessments were very costly, but monitoring became more cost-effective compared to no monitoring for higher costs involved with initial identification of carriers (screening and assessment) or lower long-term costs involved with treatment and monitoring. 5-yearly monitoring in 15-45 year olds remained the most effective cost-effective strategy for most individual variations in the cost at different stages of care, but extending the 5-yearly monitoring to all ages became cost-effective if the cost of monitoring was halved. Nevertheless, more frequent monitoring remained unlikely to be cost-effective under current thresholds even for substantial reductions in both the cost of initial clinical assessment and monitoring (Figure S3.4B).
Discounting costs and impact at 0% or 5% or adopting a shorter time horizon did also not change the conclusion about 5-yearly monitoring in under 45 year olds being the most effective cost-effective strategy (not shown).